I asked the president of International Police Mountain Bike Association this very question and here's his knowledgeable opinion :
A MTB handles the urban obstacles encountered by public safety cyclist where a road bike would not (stairs, curbs, etc.). The riggors of carrying 50 lbs of equipment for the EMS Cyclist, mainly over the rear tire is another reason. This added weight when negotiating stairs and such would not be tolerated well by a road bike. So in essence, we trade speed for functionality.
So in essence, exactly what the rest of us explained to you.